Problem: Ishaan is 16 years older than Daniel. For the last four years, Ishaan and Daniel have been going to the same school. Nine years ago, Ishaan was 3 times older than Daniel. How old is Ishaan now?
We can use the given information to write down two equations that describe the ages of Ishaan and Daniel. Let Ishaan's current age be $i$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $i = d + 16$ Nine years ago, Ishaan was $i - 9$ years old, and Daniel was $d - 9$ years old. The information in the second sentence can be expressed in the following equation: $i - 9 = 3(d - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = i - 16$ . Substituting this into our second equation, we get the equation: $i - 9 = 3($ $(i - 16)$ $ -$ $ 9)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 9 = 3i - 75$ Solving for $i$ , we get: $2 i = 66$ $i = 33$.